Grade 2 • Module 4

Addition and Subtraction Within 200 with Word Problems to 100

OVERVIEW

In Module 3 students were immersed in the base ten system, as they built a strong foundation through

a concrete to pictorial to abstract approach. They bundled groups of 10, and saw that 10 like units could

be bundled to produce a new unit that is ten times as large. They progressed from seeing 10 ones as 1

ten to understanding 10 tens as 1 hundred. Module 4 builds on that place value understanding to com-

pose and decompose place value units in addition and subtraction within 200.

Module 4 is devoted to three major areas of work. The first two are building fluency in two-digit addi-

tion and subtraction within 100 and applying that fluency to one- and two-step word problems of vary-

ing types within 100. Students’ increasing fluency with calculations within 100, begun in Grade 1, allows

word problems to transition from being mere contexts for calculation into opportunities for students to

see and analyze the relationships between quantities. Daily application problems and specific lessons in

Topics A, C, and F provide students with guided and independent practice as they negotiate a variety of

problem types, including the more complex comparison problems. Note that most two-step problems

involve single-digit addends, and do not involve the most difficult comparison problem types.

The third major area of work is developing students’ conceptual understanding of addition and subtrac-

tion of multi-digit numbers within 200 as a foundation for work with addition and subtraction within

1000 in Module 5.

In Topic A, students work with place value strategies to fluently add and subtract within 100. The final

lessons of Module 3 (finding 1 more, 1 less, 10 more, 10 less) transition into mental addition and sub-

traction of 1 and 10. Students mentally add and subtract 100 in Topics D and E, as well as during fluency

activities throughout the module, as they did in Module 3. This knowledge is then extended and used to

solve problems. For example, students might count on by ones and tens, e.g., 39 + ☐ = 62, so 40, 50, 60,

61, 62. They might use compensation, adding the same amount to the subtrahend as to the minuend to

make a multiple of ten, e.g., 62 – 39 = 63 – 40. They might add or subtract a multiple of 10 and adjust

the solution as necessary, e.g.,62 – 39 is 4 tens less than 62 but… one more (2.NBT.5). Students explain

why these strategies work using place value language, properties of addition and subtraction, and mod-

els, such as the number line .

Topic A’s strategies lead naturally to work with the written vertical algorithm for addition (Topic B) and sub-

traction (Topic C). In these two topics, students represent place value strategies with place value disks and

math drawings (see images with strategy names below). Students work with composing 1 ten from 10 ones

or decomposing 1 ten as 10 ones (with minuends within 100). After the mid-module assessment, students

continue working with manipulatives and math drawings to make sense of problems in which they compose

or decompose twice. Topic D focuses on addition, with the new complexity of composing 1 hundred from 10

tens within 200 in problems with up to four addends. Subtraction in Topic E involves subtracting when de-

composing 1 hundred for 10 tens and 1 ten for 10 ones.

Throughout the module, manipulatives and math drawings allow students to see numbers in terms of place

value units and serve as a reminder that they must add like units (e.g., knowing that 74 + 38 is 7 tens + 3

tens and 4 ones + 8 ones). The focus is often on computational strategies with bare numbers (i.e., no con-

text) so that total attention is given to understanding the value of each digit within a number, as well as why

and how the written method works. Students use the place value chart as an organizer. Simultaneous use of

a written method and a place value chart allows students to better recognize both the value of numbers

when they are not on the place value chart, and like units. The same is true when students make math

drawings and use place value language to relate each step of the drawing to a written method . The differ-

ent representations serve to solidify the understanding of the composition and decomposition of units,

moving from concrete to pictorial to abstract. Throughout the work, students are encouraged to explain

their actions and analyses, and to use the relationship between addition and subtraction to check their

work .

Throughout the module, students are encouraged to be flexible in their thinking and to use multiple strate-

gies in solving problems, including the use of drawings such as tape diagrams, which they relate to equa-

tions. In Topic F, students are introduced to the totals below method (pictured below to the far left) and are

challenged to explain why both it and the new groups below method (also pictured below to the left) work .

Abstract

students should be practicing basic addition and subtraction facts so that they may recall them with

speed and accuracy.

Terminology

New or Recently Introduced Terms

Equation

Minuend

New groups below

Place value chart (pictured below right)

Place value or number disk (pictured to the right)

Subtrahend

Totals below

Familiar Terms and Symbols

Addend

Addition

Bundle, unbundle, regroup, rename, change (compose or decompose a 10 or 100)

Difference

Hundreds place (referring to place value)

Place value (referring to the unit value of each digit in given number)

Subtraction

Units of ones, tens, hundreds, thousands (referring to place value; 10 ones is the same as 1 unit of ten)

Lesson 1

Objective: Relate 1 more, 1 less, 10 more, and 10 less to addition and subtraction of 1 and

10.

The Arrow Method

You add or subtract 1 or 10 and the arrows point to what the number becomes after you

change it. It shows that you’re changing the ones or the tens place and whether it’s more or

less. 10 more than 33 is 43, and 1 less is 42, and 1 less is 41. Then 10 less than 41 is 31, and

10 less than 31 is 21.

Lesson 2

Objective: Add and

subtract multiples of

10 including counting

on to subtract.

Lesson 3

Objective: Add and subtract multiples of 10 and some ones within 100.

.

Lesson 4

Objective: Add and subtract multiples of 10 and some ones within 100.

Sometimes we make manipulate equations to make mental addition and subtraction easier. When we add

the same amount to each number in a subtraction sentence, the

difference stays the same. You can take from one added and give

to the other to make a whole group of ten.

34 – 28 = 36 - 30

Lesson 5

Objective: Solve one- and two-step word problems within 100 using strategies

based on place value.

a. There are 31 students on the red bus. There are 29 more students on the yellow bus than on the red bus.

How many students are on the yellow bus?

b. How many students are on both buses combined?

Lesson 6

Objective: Use manipulatives to represent the composition of 10 ones as 1 ten

with two-digit addends.

You can bundling groups of ten using place value

disk or mentally.

.

Lesson 7

Objective: Relate addition using manipulatives to a written vertical method.

Notice when bundling a ten we notate it underneath the tens column.

Lesson 8

Objective: Use math drawings to represent the composition and relate drawings

to a written method.

Notice when bundling a

group of ten we notate

it underneath the tens

column.

This makes it easier for the

eye to track and for

students to see that

7+5=12 is the same as 1 ten

2 ones.

Lesson 9

Objective: Use math drawings to represent the composition when adding a two-

digit to a three-digit addend.

4 tens 12 ones can be simplified by bundling

and renaming as 5 tens 2 ones or 52. They

all have the same value.

An algorithm is a way to solve problems

using steps that help us work more quickly.

Lesson 10

Objective: Use math drawings to represent the composition when adding a two-

digit to a three-digit addend.

Lesson 11

Objective: Represent subtraction with and without the decomposition

of 1 ten as 10 ones with manipulatives.

We draw a magnifying glass

around the minuend to

show it’s the whole that we

are subtracting from.

Lesson 12

Objective: Relate manipulative representations to a written method.

Note: This shows the step by step process of subtraction. Students do

not need to recopy the problem to show the steps.

Lesson 13

Objective: Use math drawings to represent subtraction with and without decom-

position and relate drawings to a written method.

The place value chart can be simplified to a line that separates each column.

Note: This shows the step by step process of subtraction. Students do

not need to recopy the problem to show the steps.

Lesson 14

Objective: Represent subtraction with and without the decomposition when

there is a three-digit minuend.

Lesson 15

Objective: Represent subtraction with and without the decomposition

when there is a three-digit minuend.

We can use related facts to check our work.

Lesson 16

Objective: Solve one- and two-step word problems within 100 using strategies

based on place value.

3 Steps to Solving a word problem

1.. Model the Problem

Can you draw something?

What can you draw?

What conclusions can you make from your drawing?

2. Solve and write a statement.

3. Assess the solution for reasonableness.

Lesson 17

Objective: Use mental strategies to relate compositions of 10 tens as 1 hundred to 10 ones

as 1 ten.

Lesson 18

Objective: Use manipulatives to represent additions with two compositions.

Making a hundred is just like making a ten!

We can use partners to ten for both. 6 + 4 = 10, just like 6 tens + 4 tens is 10 tens, or 1 hundred. When we

put together 10 ones we make a ten, and when we put together 10 tens we make a hundred. We trade 10 of a

smaller unit for 1 of the next bigger unit: 10 ones for 1 ten and 10 tens for 1 hundred.

56 + 85

Here we changed 10 ones for 1 ten

We changed 10 tens for 1 hundred

The total of the two part is 141

Hailey and Gio solve 56 + 85. Gio says the answer is 131.

Hailey says the answer is 141. Explain whose answer is

correct using numbers, pictures, or words.

Lesson 19

Objective: Relate manipulative representations to a written method.

Students can still use

place value charts if

they need the support.

It would benefit your

child to practice flash

cards to increase their

speed and accuracy

with recalling addition

and subtraction facts.

Lesson 20

Objective: Use math drawings to represent additions with up to two composi-

tions and relate drawings to a written method.

117 Boys attended summer camp.

196 children attended summer

camp.

Lesson 21

Objective: Use math drawings to represent additions with up to two

compositions and relate drawings to a written method.

Lesson 22

Objective: Solve additions with up to four addends with totals within 200 with

and without two compositions of larger units.

Compatible numbers help us add. We always look to make a group of ten. This guides

our mental math.

Lesson 23

Objective: Use number bonds to break apart three-digit minuends and subtract

from the hundred.

Can you take out the 100?

Break apart 127 into 100 and some more.

If you take out the 100, 27 are left in 127?

Now we can subtract easily!

I know that 100 – 70 is 30. I added the 27 back on and I got 57.

20 + 27 = 57.

Lesson 24

Objective: Use manipulatives to represent subtraction with decompositions of 1

hundred as 10 tens and 1 ten as 10 ones.

136 –57

1 hundred 3 tens 6 ones

Unbundle a ten to subtract

1 hundred 2 tens 16 ones

Unbundle a hundred to subtract

12 tens 16 ones

Now that you have unbundled you can take

away 5 tens 7 ones (57)

Lesson 25

Objective: Relate manipulative representations to a written method.

Lesson 26

Objective: Use math drawings to represent

subtraction with up to two decompositions

and relate drawings to a written method.

The dot diagram is a quick tool to show the

process of unbundling to subtract.

Students should only draw one model that ends up

looking like the bottom representation.

Lesson 27

Objective: Subtract from 200 and from numbers

with zeros in the tens place.

Students have learned to unbundle a ten and a hundred to

subtract. In this lesson students learn a shortcut for

subtracting across two zeros.

Although it is more efficient to unbundle in one step

students can continue to use two steps if they find more

success with that strategy.

Lesson 28

Objective: Subtract from 200 and from numbers with zeros in the tens place.

Unbundle in one step:

There are no tens , so rename a hundred

as 9 tens and 10 ones.

That makes it 9 tens and 16 ones,

because we already had 6 ones.

Or

Unbundle in two steps:

We can change 1 hundred into 10 tens, and then change 10 tens into 9 tens 10 ones.

That makes it 9 tens and 16 ones, because we already had 6 ones.

Lesson 29

Objective: Use and explain the totals below written method using words, math

drawings, and numbers.

Method 1: New Groups Below Method 2: Totals Below

(standard algorithm) (add each unit separately)

8+3=11

20+40=60

Lesson 30

Objective: Compare totals below to new groups below as written methods.

Lesson 31

Objective: Solve two-step word problems

within 100.

1. Model the problem.

Can you draw something?

What can you draw?

What conclusions can you make from your drawing?

2. Solve and write a statement.

3. Assess the solution for reasonableness.

It’ s important to become fluent with basic addition and subtraction facts. Quick 5-10

minute activities are essential for memorization. Here are some ways to assist your child

with memorizing basic facts:

Flash Cards (both you and your child should say the fact aloud)

Counting up and down by ones and tens (begin at various numbers)

Have quick routine math talks in the car, store, and anywhere that seems appropriate.

Computer Aides such as xtramath.org

Solve a two-step add to with result un-

known word problem using a tape diagram.

Mei picked 26 berries. Luis picked 37 more

berries than Mei.

a) How many berries did Luis pick?

b) How many berries did they pick in all?